/* ----------------------------------------------------------------------
 * Project:      CMSIS DSP Library
 * Title:        xtensa_biquad_cascade_df2T_f32.c
 * Description:  Processing function for floating-point transposed direct form II Biquad cascade filter
 *
 * $Date:        27. January 2017
 * $Revision:    V.1.5.1
 *
 * Target Processor: Cortex-M cores
 * -------------------------------------------------------------------- */
/*
 * Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
 *
 * SPDX-License-Identifier: Apache-2.0
 *
 * Licensed under the Apache License, Version 2.0 (the License); you may
 * not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an AS IS BASIS, WITHOUT
 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

#include "xtensa_math.h"

/**
* @ingroup groupFilters
*/

/**
* @defgroup BiquadCascadeDF2T Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure
*
* This set of functions implements arbitrary order recursive (IIR) filters using a transposed direct form II structure.
* The filters are implemented as a cascade of second order Biquad sections.
* These functions provide a slight memory savings as compared to the direct form I Biquad filter functions.
* Only floating-point data is supported.
*
* This function operate on blocks of input and output data and each call to the function
* processes <code>blockSize</code> samples through the filter.
* <code>pSrc</code> points to the array of input data and
* <code>pDst</code> points to the array of output data.
* Both arrays contain <code>blockSize</code> values.
*
* \par Algorithm
* Each Biquad stage implements a second order filter using the difference equation:
* <pre>
*    y[n] = b0 * x[n] + d1
*    d1 = b1 * x[n] + a1 * y[n] + d2
*    d2 = b2 * x[n] + a2 * y[n]
* </pre>
* where d1 and d2 represent the two state values.
*
* \par
* A Biquad filter using a transposed Direct Form II structure is shown below.
* \image html BiquadDF2Transposed.gif "Single transposed Direct Form II Biquad"
* Coefficients <code>b0, b1, and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients.
* Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients.
* Pay careful attention to the sign of the feedback coefficients.
* Some design tools flip the sign of the feedback coefficients:
* <pre>
*    y[n] = b0 * x[n] + d1;
*    d1 = b1 * x[n] - a1 * y[n] + d2;
*    d2 = b2 * x[n] - a2 * y[n];
* </pre>
* In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.
*
* \par
* Higher order filters are realized as a cascade of second order sections.
* <code>numStages</code> refers to the number of second order stages used.
* For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages.
* A 9th order filter would be realized with <code>numStages=5</code> second order stages with the
* coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>).
*
* \par
* <code>pState</code> points to the state variable array.
* Each Biquad stage has 2 state variables <code>d1</code> and <code>d2</code>.
* The state variables are arranged in the <code>pState</code> array as:
* <pre>
*     {d11, d12, d21, d22, ...}
* </pre>
* where <code>d1x</code> refers to the state variables for the first Biquad and
* <code>d2x</code> refers to the state variables for the second Biquad.
* The state array has a total length of <code>2*numStages</code> values.
* The state variables are updated after each block of data is processed; the coefficients are untouched.
*
* \par
* The CMSIS library contains Biquad filters in both Direct Form I and transposed Direct Form II.
* The advantage of the Direct Form I structure is that it is numerically more robust for fixed-point data types.
* That is why the Direct Form I structure supports Q15 and Q31 data types.
* The transposed Direct Form II structure, on the other hand, requires a wide dynamic range for the state variables <code>d1</code> and <code>d2</code>.
* Because of this, the CMSIS library only has a floating-point version of the Direct Form II Biquad.
* The advantage of the Direct Form II Biquad is that it requires half the number of state variables, 2 rather than 4, per Biquad stage.
*
* \par Instance Structure
* The coefficients and state variables for a filter are stored together in an instance data structure.
* A separate instance structure must be defined for each filter.
* Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.
*
* \par Init Functions
* There is also an associated initialization function.
* The initialization function performs following operations:
* - Sets the values of the internal structure fields.
* - Zeros out the values in the state buffer.
* To do this manually without calling the init function, assign the follow subfields of the instance structure:
* numStages, pCoeffs, pState. Also set all of the values in pState to zero.
*
* \par
* Use of the initialization function is optional.
* However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
* To place an instance structure into a const data section, the instance structure must be manually initialized.
* Set the values in the state buffer to zeros before static initialization.
* For example, to statically initialize the instance structure use
* <pre>
*     xtensa_biquad_cascade_df2T_instance_f32 S1 = {numStages, pState, pCoeffs};
* </pre>
* where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer.
* <code>pCoeffs</code> is the address of the coefficient buffer;
*
*/

/**
* @addtogroup BiquadCascadeDF2T
* @{
*/

/**
* @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
* @param[in]  *S        points to an instance of the filter data structure.
* @param[in]  *pSrc     points to the block of input data.
* @param[out] *pDst     points to the block of output data
* @param[in]  blockSize number of samples to process.
* @return none.
*/


void xtensa_biquad_cascade_df2T_f32(
const xtensa_biquad_cascade_df2T_instance_f32 * S,
float32_t * pSrc,
float32_t * pDst,
uint32_t blockSize)
{

   float32_t *pIn = pSrc;                         /*  source pointer            */
   float32_t *pOut = pDst;                        /*  destination pointer       */
   float32_t *pState = S->pState;                 /*  State pointer             */
   float32_t *pCoeffs = S->pCoeffs;               /*  coefficient pointer       */
   float32_t acc1;                                /*  accumulator               */
   float32_t b0, b1, b2, a1, a2;                  /*  Filter coefficients       */
   float32_t Xn1;                                 /*  temporary input           */
   float32_t d1, d2;                              /*  state variables           */
   uint32_t sample, stage = S->numStages;         /*  loop counters             */




   do
   {
      /* Reading the coefficients */
      b0 = *pCoeffs++;
      b1 = *pCoeffs++;
      b2 = *pCoeffs++;
      a1 = *pCoeffs++;
      a2 = *pCoeffs++;

      /*Reading the state values */
      d1 = pState[0];
      d2 = pState[1];


      sample = blockSize;

      while (sample > 0U)
      {
         /* Read the input */
         Xn1 = *pIn++;

         /* y[n] = b0 * x[n] + d1 */
         acc1 = (b0 * Xn1) + d1;

         /* Store the result in the accumulator in the destination buffer. */
         *pOut++ = acc1;

         /* Every time after the output is computed state should be updated. */
         /* d1 = b1 * x[n] + a1 * y[n] + d2 */
         d1 = ((b1 * Xn1) + (a1 * acc1)) + d2;

         /* d2 = b2 * x[n] + a2 * y[n] */
         d2 = (b2 * Xn1) + (a2 * acc1);

         /* decrement the loop counter */
         sample--;
      }

      /* Store the updated state variables back into the state array */
      *pState++ = d1;
      *pState++ = d2;

      /* The current stage input is given as the output to the next stage */
      pIn = pDst;

      /*Reset the output working pointer */
      pOut = pDst;

      /* decrement the loop counter */
      stage--;

   } while (stage > 0U);


}

/**
   * @} end of BiquadCascadeDF2T group
   */
